Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies
Number Theory
2025-03-04 v1
Abstract
W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to -dimensional balls. In this paper, we extend their result to any -dimensional convex body with a smooth boundary and finite order of contact. As an intermediate step, we prove a geometric inequality for the Fourier transform of the characteristic function of a convex body.
Keywords
Cite
@article{arxiv.2503.00973,
title = {Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies},
author = {Luca Brandolini and Leonardo Colzani and Giancarlo Travaglini},
journal= {arXiv preprint arXiv:2503.00973},
year = {2025}
}